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Machine learning in drug discovery has been focused on virtual screening of molecular libraries using discriminative models. Generative models are an entirely different approach that learn to represent and optimize molecules in a continuous…
In this paper, we present a fast algorithm for constructing a concept (Galois) lattice of a binary relation, including computing all concepts and their lattice order. We also present two efficient variants of the algorithm, one for…
We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of $\mathbb{N}^{d}$ with finite complement in $\mathbb{N}^{d}$. These semigroups are affine semigroups, which in particular implies…
The discovery of new functional and stable materials is a big challenge due to its complexity. This work aims at the generation of new crystal structures with desired properties, such as chemical stability and specified chemical…
The design of molecules and materials with tailored properties is challenging, as candidate molecules must satisfy multiple competing requirements that are often difficult to measure or compute. While molecular structures, produced through…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Deep generative models are able to suggest new organic molecules by generating strings, trees, and graphs representing their structure. While such models allow one to generate molecules with desirable properties, they give no guarantees…
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…
Nanoparticles with "sticky patches" have long been proposed as building blocks for the self-assembly of complex structures. The synthetic realizability of such patchy particles, however, greatly lags behind predictions of patterns they…
With the recent advances in machine learning for quantum chemistry, it is now possible to predict the chemical properties of compounds and to generate novel molecules. Existing generative models mostly use a string- or graph-based…
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in…
Polynomial reconstruction on Cartesian grids is fundamental in many scientific and engineering applications, yet it is still an open problem how to construct for a finite subset $K$ of $\mathbb{Z}^{\textsf{D}}$ a lattice $\mathcal{T}\subset…
The goal of structure-based drug discovery is to find small molecules that bind to a given target protein. Deep learning has been used to generate drug-like molecules with certain cheminformatic properties, but has not yet been applied to…
Crystal structures can be simplified as a periodic point set that repeats across three-dimensional space along an underlying lattice. Traditionally, crystal representation methods characterize the structure using descriptors such as lattice…
We give a new algorithm for generating Greechie diagrams with arbitrary chosen number of atoms or blocks (with 2,3,4,... atoms) and provide a computer program for generating the diagrams. The results show that the previous algorithm does…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
Deep generative models have been applied with increasing success to the generation of two dimensional molecules as SMILES strings and molecular graphs. In this work we describe for the first time a deep generative model that can generate 3D…
Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and…
Determination of crystal structures of nanocrystalline or amorphous compounds is a great challenge in solid states chemistry and physics. Pair distribution function (PDF) analysis of X-Ray or neutron total scattering data has proven to be a…
A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is…